We describe a compressive projection algorithm and quantitatively assess its performance when used with a Hyperspectral Image Projector (HIP). The HIP is being developed by NIST for system-level performance testing of hyperspectral and multispectral imagers, including the instrument, its calibration, and any associated spectral unmixing algorithms. It projects a two-dimensional image into the unit under test (UUT), whereby each pixel can have an independently programmable arbitrary spectrum. The HIP hardware consists of a spectral engine optically in series with a spatial engine. The spectral engine produces the light corresponding to a series of programmable spectra that could be, for example, the endmember spectra of a real hyperspectral image cube that is to be projected. The spectral engine uniformly illuminates the spatial engine with such spectra sequentially. The spatial engine, in turn, maps each endmember spectrum in the correct proportions, such as determined by a corresponding set of two-dimensional spatial abundance images. To efficiently project a single frame of dynamic realistic hyperspectral imagery through the collimator into the UUT, a compression algorithm has been developed whereby the series of abundance images and corresponding endmember spectra that comprise the image cube of that frame are first computed using an automated endmember-finding algorithm such as the Sequential Maximum Angle Convex Cone (SMACC) endmember model. Then these endmember spectra are projected sequentially on the spectral engine in sync with the projection of the abundance images on the spatial engine, during the single-frame exposure time of the UUT.